# Contents at a Glance

Document Sample

```					                       Contents at a Glance
Introduction .............................................................................1
Part I: Back to Basics with Basic Math......................................5
Chapter 1: We’ve Got Your Numbers...................................................................................................7
Chapter 2: Smooth Operators: Working with the Big Four Operations ........................................23

AL
Chapter 3: Getting Down with Negative Numbers...........................................................................37
Chapter 4: It’s Just an Expression......................................................................................................49

RI
Chapter 5: Dividing Attention: Divisibility, Factors, and Multiples ...............................................69

TE
Part II: Slicing Things Up: Fractions, Decimals, and Percents ....89
Chapter 6: Fractions Are a Piece of Cake..........................................................................................91

MA
Chapter 7: Fractions and the Big Four ............................................................................................107
Chapter 8: Getting to the Point with Decimals...............................................................................141
Chapter 9: Playing the Percentages.................................................................................................163
D
Part III: A Giant Step Forward: Intermediate Topics ................175
TE

Chapter 10: Seeking a Higher Power through Scientific Notation ...............................................177
Chapter 11: Weighty Questions on Weights and Measures ..........................................................187
Chapter 12: Shaping Up with Geometry..........................................................................................201
GH

Chapter 13: Getting Graphic: Cartesian Graphs.............................................................................221

Part IV: The X Factor: Introducing Algebra .............................233
RI

Chapter 14: Expressing Yourself with Algebraic Expressions......................................................235
Chapter 15: Finding the Right Balance: Solving Algebraic Equations .........................................255
PY

Part V: The Part of Tens ........................................................271
CO

Chapter 16: Ten Alternative Numeral and Number Systems........................................................273
Chapter 17: Ten Curious Types of Numbers ..................................................................................281

Index ...................................................................................287
Introduction..............................................................................1
Conventions Used in This Book.........................................................................................2
Foolish Assumptions...........................................................................................................2
How This Book Is Organized ..............................................................................................2
Part I: Back to Basics with Basic Math....................................................................2
Part II: Slicing Things Up: Fractions, Decimals, and Percents..............................3
Part III: A Giant Step Forward: Intermediate Topics..............................................3
Part IV: The X Factor: Introducing Algebra ............................................................3
Part V: The Part of Tens ............................................................................................3
Icons Used in This Book .....................................................................................................4
Where to Go from Here .......................................................................................................4

Part I: Back to Basics with Basic Math ......................................5
Chapter 1: We’ve Got Your Numbers .............................................................................7
Getting in Place with Numbers and Digits........................................................................7
Rollover: Rounding Numbers Up and Down ..................................................................10
Using the Number Line with the Big Four ......................................................................12
The Column Lineup: Adding and Subtracting................................................................14
Multiplying Multiple Digits ...............................................................................................15
Cycling through Long Division.........................................................................................17
Solutions to We’ve Got Your Numbers............................................................................19

Chapter 2: Smooth Operators: Working with the Big Four Operations.................23
Switching Things Up with Inverse Operations and the Commutative Property .......23
Getting with the In-Group: Parentheses and the Associative Property......................27
Becoming Unbalanced: Inequalities ................................................................................30
Special Times: Powers and Square Roots.......................................................................32
Answers to Problems in Smooth Operators...................................................................34

Chapter 3: Getting Down with Negative Numbers ...................................................37
Understanding Where Negative Numbers Come From.................................................37
Sign-Switching: Understanding Negation and Absolute Value .....................................39
Subtracting with Negative Numbers ...............................................................................42
Comparing Signs of the Times (And Division) of Negative Numbers .........................43
Answers to Problems in Getting Down with Negative Numbers .................................45
x   Basic Math & Pre-Algebra Workbook For Dummies

Chapter 4: It’s Just an Expression................................................................................49
Evaluating Expressions with Addition and Subtraction ...............................................49
Evaluating Expressions with Multiplication and Division ............................................51
Making Sense of Mixed-Operator Expressions ..............................................................52
Handling Powers Responsibly .........................................................................................53
Prioritizing Parentheses ...................................................................................................54
Pulling Apart Parentheses and Powers...........................................................................56
Figuring Out Nested Parentheses ....................................................................................57
Bringing It All Together: The Order of Operations........................................................59
Solutions to It’s Just an Expression.................................................................................60

Chapter 5: Dividing Attention: Divisibility, Factors, and Multiples .......................69
Checking for Leftovers: Divisibility Tests.......................................................................69
Understanding Factors and Multiples.............................................................................72
One Number, Indivisible: Identifying Prime (And Composite) Numbers ...................73
Generating a Number’s Factors .......................................................................................75
Decomposing a Number into Its Prime Factors.............................................................77
Finding the Greatest Common Factor (GCF)..................................................................79
Generating the Multiples of a Number............................................................................81
Finding the Least Common Multiple (LCM) ...................................................................82
Solutions to Divisibility, Factors, and Multiples ............................................................84

Part II: Slicing Things Up: Fractions, Decimals, and Percents.....89
Chapter 6: Fractions Are a Piece of Cake ..................................................................91
Getting Down the Basic Fraction Stuff ............................................................................91
In Mixed Company: Converting between Mixed Numbers and
Improper Fractions ........................................................................................................94
Increasing and Reducing the Terms of Fractions ..........................................................97
Comparing Fractions with Cross-Multiplication..........................................................100
Solutions to Fractions Are a Piece of Cake...................................................................102

Chapter 7: Fractions and the Big Four.......................................................................107
Multiplying Fractions: A Straight Shot..........................................................................107
Flipping for Fraction Division.........................................................................................109
Reaching the Common Denominator: Adding Fractions ............................................111
The Other Common Denominator: Subtracting Fractions .........................................115
Multiplying and Dividing Mixed Numbers....................................................................118
Borrowing from the Whole: Subtracting Mixed Numbers ..........................................123
Solutions to Fractions and the Big Four .......................................................................127

Chapter 8: Getting to the Point with Decimals........................................................141
Getting in Place: Basic Decimal Stuff.............................................................................141
Knowing Simple Decimal-Fraction Conversions..........................................................144
A New Lineup: Adding and Subtracting Decimals .......................................................146
Counting Decimal Places: Multiplying Decimals .........................................................148
Decimal Points on the Move: Dividing Decimals .........................................................149
Changing Decimals to Fractions ....................................................................................151
Changing Fractions to Decimals ....................................................................................153
Solutions to Getting to the Point with Decimals..........................................................155

Chapter 9: Playing the Percentages..........................................................................163
Converting Percents to Decimals ..................................................................................163
Changing Decimals to Percents .....................................................................................165
Switching from Percents to Fractions...........................................................................166
Converting Fractions to Percents..................................................................................167
Mixing Things Up with the Percent Circle....................................................................169
Solutions to Playing the Percentages............................................................................172

Part III: A Giant Step Forward: Intermediate Topics.................175
Chapter 10: Seeking a Higher Power through Scientific Notation .....................177
On the Count of Zero: Understanding Powers of Ten .................................................177
Exponential Arithmetic: Multiplying and Dividing Powers of Ten ............................180
Representing Numbers in Scientific Notation..............................................................181
Multiplying and Dividing with Scientific Notation.......................................................182
Answers to Problems in Seeking a Higher Power through Scientific Notation .......184

Chapter 11: Weighty Questions on Weights and Measures .................................187
The Basics of the English System ..................................................................................187
Going International with the Metric System ................................................................190
Converting between English and Metric Units ............................................................193
Answers to Problems in Weighty Questions on Weights and Measures ..................195

Chapter 12: Shaping Up with Geometry....................................................................201
Getting in Shape: Polygon (And Nonpolygon) Basics.................................................201
Making a Triple Play with Triangles ..............................................................................202
Taking a Fourth Side with Quadrilaterals.....................................................................205
Getting Around with Circle Measurements ..................................................................210
Building Solid Measurement Skills ................................................................................212
Answers to Problems in Shaping Up with Geometry ..................................................217

Chapter 13: Getting Graphic: Cartesian Graphs ......................................................221
Getting the Point of the Cartesian Graph .....................................................................221
Drawing the Line on the Cartesian Graph ....................................................................225
Answers to Problems in Getting Graphic: Cartesian Graphs.....................................228

Part IV: The X Factor: Introducing Algebra..............................233
Chapter 14: Expressing Yourself with Algebraic Expressions.............................235
Plug It In: Evaluating Algebraic Expressions ................................................................236
Knowing the Terms of Separation .................................................................................237
Adding and Subtracting Similar Terms .........................................................................239
Multiplying and Dividing Terms.....................................................................................240
xii   Basic Math & Pre-Algebra Workbook For Dummies

Simplifying Expressions by Combining Similar Terms ...............................................242
Simplifying Expressions with Parentheses...................................................................244
FOILing: Dealing with Two Sets of Parentheses...........................................................245
Answers to Problems in Expressing Yourself with Algebraic Expressions ..............248

Chapter 15: Finding the Right Balance: Solving Algebraic Equations................255
Solving Simple Algebraic Equations..............................................................................255
Equality for All: Using the Balance Scale to Isolate x..................................................258
Switching Sides: Rearranging Equations to Isolate x ..................................................259
Barring Fractions: Cross-Multiplying to Simplify Equations ......................................261
Answers to Problems in Finding the Right Balance: Solving
Algebraic Equations.....................................................................................................264

Part V: The Part of Tens.........................................................271
Chapter 16: Ten Alternative Numeral and Number Systems ................................273
Tally Marks .......................................................................................................................273
Bundled Tally Marks........................................................................................................274
Egyptian Numerals ..........................................................................................................274
Babylonian Numerals ......................................................................................................275
Ancient Greek Numerals .................................................................................................275
Roman Numerals .............................................................................................................276
Mayan Numerals ..............................................................................................................276
Base 2, or Binary Numbers.............................................................................................277
Prime-Based Numbers ....................................................................................................279

Chapter 17: Ten Curious Types of Numbers..............................................................281
Square Numbers ..............................................................................................................281
Triangular Numbers ........................................................................................................282
Cubic Numbers ................................................................................................................283
Factorial Numbers ...........................................................................................................283
Powers of Two..................................................................................................................284
Perfect Numbers ..............................................................................................................284
Amicable Numbers ..........................................................................................................285
Prime Numbers ................................................................................................................285
Mersenne Primes .............................................................................................................286
Fermat Primes ..................................................................................................................286

Index....................................................................................287

```
DOCUMENT INFO
Shared By:
Categories:
Stats:
 views: 15 posted: 2/17/2010 language: English pages: 6